The average daily temperature, t, in degrees fahrenheit for a city as a function of the month of the year, m, can be modeled by the equation t = 35 cosine (startfraction pi over 6 endfraction (m 3) 55, where m = 0 represents january 1, m = 1 represents february 1, m = 2 represents march 1, and so on. which equation also models this situation?

Respuesta :

The answer will be t = [tex]sin((m.\frac{\pi}{6})+55)[/tex] average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year.

What is temperature?

Temperature is the degree or intensity of heat present in a substance or object, especially as expressed according to a comparative scale and shown by a thermometer or perceived by touch.

TO SOLVE:

[tex]35cos(\frac{\pi}{6(m+3)}+55)\\\\35 cos(\frac{\pi m}{6} + 55 + \frac{\pi}{2})\\[/tex]

suppose [tex]x = m.\frac{\pi}{6}+55[/tex] and [tex]\frac{\pi}{2} = 90[/tex] degree

We know, cos(x+90°) = - sin(X)

⇒ [tex]cos((m.\frac{\pi}{6})+55+90degree)[/tex]degree = -[tex]sin((m.\frac{\pi}{6})+55)[/tex]

⇒ t = [tex]sin((m.\frac{\pi}{6})+55)[/tex]

Hence the answer will be t = [tex]sin((m.\frac{\pi}{6})+55)[/tex] average daily temperature, t, in degrees Fahrenheit for a city as a function of the month of the year.

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